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cat Skill: Derivational Pipe Chaining
Basado en la clasificación ocupacional SOC
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Bridge active inference theory with robot control using K-Scale's JAX/MuJoCo stack. Use when connecting predictive coding to locomotion policies, mapping KL divergence minimization to RL training, applying mean field approximation to robotics state estimation, or implementing sim2real as inference about future observations.
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| name | cat |
| description | cat Skill: Derivational Pipe Chaining |
| version | 1.0.0 |
Trit: 0 (ERGODIC - coordinator) Color: #26D826 (Green) Principle: Chain operations via derivational succession, not temporal
The cat skill implements the |> pipe operator using derivational chaining instead of temporal succession. Each pipe stage advances a seed: seed_{n+1} = f(seed_n, trit_n).
pipe_chain: A |> f |> g |> h
seed₀ → f(seed₀, trit_f) → seed₁
seed₁ → g(seed₁, trit_g) → seed₂
seed₂ → h(seed₂, trit_h) → seed₃
GF(3) conservation: Σ(trit_f + trit_g + trit_h) ≡ 0 (mod 3)
(ns cat.pipe
(:require [clojure.string :as str]))
(def GAMMA 0x9E3779B97F4A7C15)
(def MIX 0xBF58476D1CE4E5B9)
(def MASK64 0xFFFFFFFFFFFFFFFF)
(defn chain-seed [seed trit]
(bit-and (unchecked-multiply
(bit-xor seed (* trit GAMMA))
MIX)
MASK64))
(defmacro |>
"Derivational pipe with GF(3) tracking"
[seed & forms]
(reduce (fn [acc [f trit]]
`(let [result# (~f ~acc)
new-seed# (chain-seed (:seed ~acc) ~trit)]
(assoc result# :seed new-seed# :trit ~trit)))
`{:value ~seed :seed 0x42D :trit 0}
(partition 2 forms)))
# Pipe with GF(3) conservation
bb -e "(require '[cat.pipe :refer [|>]])
(|> 'input'
[read-fn -1] ; MINUS: validate
[transform-fn 0] ; ERGODIC: coordinate
[write-fn +1]) ; PLUS: generate
; => GF(3) sum = 0 ✓"
# Run pipe chain
just cat-pipe 'input' -1 0 +1
# Verify GF(3) conservation
just cat-verify-gf3 chain.edn
Forms triads with temporal-coalgebra (-1) and synthetic-adjunctions (+1):
temporal-coalgebra (-1) ⊗ cat (0) ⊗ synthetic-adjunctions (+1) = 0 ✓
Skill Name: cat
Type: Pipe Coordinator
Trit: 0 (ERGODIC)
Replaces: dypler-mcp (not found in npm)
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
category-theory: 139 citations in bib.duckdbThis skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Concepts: generic arithmetic, coercion, symbolic, numeric
cat (−) + SDF.Ch3 (○) + [balancer] (+) = 0
Skill Trit: -1 (MINUS - verification)
Generic arithmetic crosses type boundaries. This skill handles heterogeneous data.
This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.